No. project to 2-d, say the 2-d box has dimension w and h. that means there must exist two numbers (n,m), n,m = 0,1,2,....
n * cos(a) = w
and
m * sin(a) = h

a is the angle between the vilocity and the box wall.
there are nly limited number of angle a can satisfy this consition.

same to 3-d.